Many three-dimensional N = 2 SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS 4 magnetically charged black holes in Mtheory and massive type IIA string theory. In this context we also discuss novel AdS 2 solutions of eleven-dimensional supergravity which describe the near horizon region of large new families of supersymmetric black holes arising from M2-branes wrapping Riemann surfaces.

We provide for the first time the exact solution of Maxwell's equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard-Wiechert field the electromagnetic field acquires singular δ-like contributions whose support and dimensionality depend crucially on whether the motion is a) linear, b) accelerated unbounded, c) accelerated bounded. In the first two cases the particle generates a planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string.

We determine for the first time the electromagnetic field generated by a generic massless accelerated charge, solving exactly Maxwell's equations. This result may shed new light on the possible existence of such particles in nature.

We derive a metric-like Lagrangian and equations of motion, in AdS space, for multiplets of fermionic fields with spin ranged from 1/2 to s, from their frame-like formulation.Comment: 1+13 pages, v3: typos corrected, references adde